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ECON1003 S1 2023

Problem Set 5

1. Calculate the integral for the following:

a. x + x3 + x3.5

b.

c. x2 | 1+   2    |

d. 

Q

2Q−5

e.

Q

2. Integrate the following:

a. j 5  dY                                   b. j (1+0.8t)1.12 dt

c. j e12xdx                                            d. j 4 e2x dx

e. j 100(1−e−0.5Y)dY                           f. j dx

3. Using the method of integration by substitution, find the integral j dx

4. Evaluate the following jt40e−0.3tdt

5. Find the particular solution for the following differential equations: (a) dy/dx = 5x given y = 4 when x = 2.

(b) dy/dt − 10t − 2 = 0 given y = 15 and t = 0.